MEAN VALUE THEOREMS FOR AUTOMORPHIC L-FUNCTIONS

被引：15
作者：
Fomenko, O. M. [1 ]
机构：
[1] Russian Acad Sci, VA Steklov Math Inst, St Petersburg Branch, St Petersburg 191023, Russia
来源：
ST PETERSBURG MATHEMATICAL JOURNAL | 2008年 / 19卷 / 05期
关键词：
Symmetric square L-function; summatory function; Euler product; Voronoi formula; mean value;
D O I：
10.1090/S1061-0022-08-01024-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let f be a holomorphic Hecke eigencuspform of even weight k >= 12 for SL(2, Z) and let L(s, sym(2) f) be the symmetric square L-function of f. Let C(s) be the summatory function of the coefficients of L(s, sym(2) f). The true order is found for integral C-x(0)(y)(2)dy.
引用
收藏
页码：853 / 866
页数：14
相关论文
共 30 条
[1]   SYMMETRICAL SQUARE L-FUNCTIONS ON GL(R) [J].
BUMP, D ;
GINZBURG, D .
ANNALS OF MATHEMATICS, 1992, 136 (01) :137-205
[2]   ON THE MEAN VALUE OF THE ERROR TERM FOR A CLASS OF ARITHMETICAL FUNCTIONS [J].
CHANDRASEKHARAN, K ;
NARASIMHAN, R .
ACTA MATHEMATICA, 1964, 112 (1-2) :41-67
[3]   On two sentences by Herr G.H Hardy [J].
Cramer, H .
MATHEMATISCHE ZEITSCHRIFT, 1922, 15 :201-210
[4]   On the mean square of the error term for an extended Selberg class [J].
De Roton, Anne .
ACTA ARITHMETICA, 2007, 126 (01) :27-55
[5]  
DEVENPORT H, 1935, J LOND MATH SOC, V10, P136
[6]  
Fomenko O., 2007, J MATH SCI-U TOKYO, V143, P3174
[7]  
Fomenko OM., 2006, J. Math. Sci, V133, P1749, DOI [10.1007/s10958-006-0086-x, DOI 10.1007/S10958-006-0086-X]
[8]  
GELBART S, 1978, ANN SCI ECOLE NORM S, V11, P471
[9]  
GELBART S, 1988, ANAL PROPERTIES AUTO
[10]  
HAFNER JL, 1981, LECT NOTES MATH, V899, P148
123